if a body describes a vertical circle then the minimum velocity at an angle theta from the lowest position is
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if a body describes a vertical circle then the minimum velocity at an angle theta from the lowest position is
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Answer:
The answer is Vb - √5gr.
Step-by-step explanation:
When a body is moving in a vertical circle, it must satisfy the constraints of centripetal force to remain in a circle. Also, the conservation energy has to be satisfied. So the total energy kinetic + potential must be equal at all points.
At the top, the minimum velocity should be such that at least the centripetal force is equal to the weight of the body. So we have
av^2top/r = mg
Vtop = √gr
So the minimum velocity at the top is Vtop - √gr.
At the bottom from the conservation of energy we get,
1/2mVb^2 = mgh + 1/2mvtop^2
Vb^2 = 4gr + gr (Since h =2r)
Vb = √gh + 2gr = √5gr
Vb = √5gr.
Thus the minimum velocity at the bottom is Vb - √5gr.